Q: Which of the following is an example of a piecewise defined function?

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \\ x & x \geq 0 \end{cases}$$

Question 1

Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \u003c 6$$?

Accepted Answer

$$\{ x \mid 1 \u003c x \u003c 6 \}$$

Question 2

Which of the following numbers has a finite decimal expansion?

Accepted Answer

$$\frac{1}{4}$$

Question 3

Suppose $$f(x) = \sqrt{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 4

Which of the following best describes a function?

Accepted Answer

A rule which assigns to each value in the domain exactly one value in the range.

Question 5

Given the function $$f(x) = 2x + 3$$, what is the slope of its graph?

Accepted Answer

$$2$$

Question 6

Which of the following statements about real numbers is TRUE?

Accepted Answer

Every real number can be represented by an infinite decimal expansion.

Question 7

If $$f(x) = \frac{1}{x}$$, which of the following is NOT in the domain of $$f$$?

Accepted Answer

$$0$$

Question 8

A function $$f is $$defined by $$f(x) = x^2$ - 4x + 3. $$What is the range of $$f$$?

Accepted Answer

$$[ -1, \infty )$$

Question 9

Which of the following is the correct set notation for the interval including all real numbers $$x$$ such that $$x \geq 2$$?

Accepted Answer

$$\{ x \mid x \geq 2 \}$$

Question 10

Suppose you are modeling the height $$h (in $$meters) of a ball thrown upward from the ground as a function of time $$t (in $$seconds) by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached by the ball?

Accepted Answer

$$20.41$$ meters

Question 11

Which of the following is the correct definition of the distance between two real numbers $$a$$ and $$b$$?

Accepted Answer

$$|a - b|$$

Question 12

Which of the following is the graph of a function?

Accepted Answer

A curve in the plane that passes the vertical line test.

Question 13

If $$f(x) = \sqrt{9 - x^2$}$$, what is the domain of $$f$$?

Accepted Answer

$$[-3, 3]$$

Question 14

A real-world application: The temperature $$T (in$$ $$^\circC) of a $$chemical reaction is modeled by $$T(t) = 25 + 10e$$^{-0.5t}$$, where t$ is time in minutes. What is the temperature as t$$ 	o \infty$$?

Accepted Answer

$$25^\circC$$

Question 15

Which of the following is an example of a piecewise defined function?

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \ x & x \geq 0 \end{cases}$$

Question 16

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 17

Which of the following intervals represents all $$x$$ such that $$-2 \leq x \u003c 5$$?

Accepted Answer

$$[-2, 5)$$

Question 18

A function $$f is $$defined on $$[0, 10]$$ and models the amount of a drug in the bloodstream (in mg) over time $$t (in $$hours). If $$f(0) = 0$$ and $$f(10) = 0$$, which of the following is a plausible interpretation?

Accepted Answer

The drug is administered at $$t=0$$, reaches a peak, and is eliminated by $$t=10.$$

Question 19

Which of the following is the correct set notation for the set of all rational numbers?

Accepted Answer

$$\mathbb{Q}$$

Question 20

Suppose $$f(x) = \frac{1}{x-1}. $$For which value of $$x is$$ $$f(x)$$ undefined?

Accepted Answer

$$x = 1$$

MATH 221: First Semester Calculus – Numbers, Functions, and Foundations

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